SOLUTION: State all the values of x that satisfy the following equation: {{{ (7-2/x)=sqrt(7/x) }}}

Algebra ->  Expressions-with-variables -> SOLUTION: State all the values of x that satisfy the following equation: {{{ (7-2/x)=sqrt(7/x) }}}      Log On


   

Question 1097458: State all the values of x that satisfy the following equation: +%287-2%2Fx%29=sqrt%287%2Fx%29+
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
square both sides
49-28/x+ (4/x^2)=7/x
49+(4/x^2)=(35/x)
multiply everything by x^2
49x^2+4=35x
49x^2-35x+4=0
(7x-4)(7x-1)=0
x=(4/7), (1/7)
check
7-(14/4)=sqrt(49/4)
3.5=7/2=3.5
check
7-14=sqrt(49)
sqrt(49)=7 by convention, the principal square root.
Therefore, x=(4/7) is the value.